Description

For Bessie the cow’s birthday, Farmer John has given her free reign over one of his best fields to eat grass.

The field is covered in N patches of grass (1≤N≤1000), conveniently numbered 1…N, that each have a distinct

quality value. If Bessie eats grass of quality Q, she gains Q units of energy. Each patch is connected to up to 10

neighboring patches via bi-directional paths, and it takes Bessie E units of energy to move between adjacent

patches (1≤E≤1,000,000). Bessie can choose to start grazing in any patch she wishes, and she wants to stop

grazing once she has accumulated a maximum amount of energy.

Unfortunately, Bessie is a picky bovine, and once she eats grass of a certain quality, she’ll never eat grass at or

below that quality level again! She is still happy to walk through patches without eating their grass; in fact, she

might find it beneficial to walk through a patch of high-quality grass without eating it, only to return later for a tasty snack.

Please help determine the maximum amount of energy Bessie can accumulate.

为了庆祝贝茜的生日,FJ给她吃草的自由. N块草地,标号1到N(1<=N<=1000),草地有营养价值.当贝茜走到这个草地,可以获得等于这块草地的营养价值的能量. 每块草地最多有10条双向边,每走一条边,贝茜花费E的能量. 贝茜拿可以从任何地方出发,当她不能获得更多的能量的时候她就会停止. 然而因为贝茜挑食,她每次不会吃低于或等于上次的营养价值的草地,所以她获得的能量是严格上升的,当然她可以选择只是经过一块草地而不吃草.

算出贝茜能够获得的最大能量.

Format

Input

The first line of input contains N and E. Each of the remaining N lines describe a patch of grass.

They contain two integers Q and D giving the quality of the patch (in the range 1…1,000,000) and

its number of neighbors. The remaining D numbers on the line specify the neighbors.

第一排两个数 N和E

剩下N排,每排包含Q,D两个数字,Q代表这个草地的营养价值,D代表这个点的边数,剩下D个数表示于这块草地相邻的草地.

Output

Please output the maximum amount of energy Bessie can accumulate.

一个整数

最大权值

Samples

5 2
4 1 2
1 3 1 3 4
6 2 2 5
5 2 2 5
2 2 3 4

7

Limitation

Bessie starts at patch 4 gaining 5 units of energy from the grass there. She then takes the path to patch 5 losing 2 units of energy during her travel. She refuses to eat the lower quality grass at patch 5 and travels to patch 3 again losing 2 units of energy. Finally she eats the grass at patch 3 gaining 6 units of energy for a total of 7 energy. Note tha the sample case above is different from test case 1 when you submit.